課程名稱︰個體經濟學二
課程性質︰必修
課程教師︰古慧雯
開課學院：社會科學院
開課系所︰經濟學系
考試日期（年月日）︰99.06.21
考試時限（分鐘）：13:20-15:20 (120min)
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
總分42分。答題皆須附說明，未做解釋的答案概不計分。
1.Producer A, a price taker, employs two factors L and K to produce y, the
production function is:
y=√(LK).
Let PL, PK and Py denote the prices of L, K, and y.
(a)(2pt) Are L and K substitutes or complements in production?
(b)(2pt) In the short run, K is fixed to be 100 units, while th quantity of
L is free to adjust. What is A's demend for L, D(PL)?
(c)(4pt) In the long run, the quantity of K is also free to adjust. When PL
increase, how will A adjust the production plan (L,K,y)? (You only have
to analyze the directions of changes.
2.There are two types of people. A type A person has an income of $10 in the
first period and $20 in the second period. A type B person has an income of
$20 in the first period and $10 in the second period. Every one has the same
same utility function:
u=(c1^2)(c2),
where ci is the consumption in the i-th period. There are 100 type A people
and 100 type B people. Let r denote the inter-temporal interest rate.
(a)(2pt) What is a type A person's budget constraint when making the inter-
temporal consumption decision?
(b)(2pt) If a type A person consumes his endowment, what is his marginal
rate of substitution MRSA(≡|dc2/dc1|)?
(c)(2pt) What kind of an interest rate will cause a type A person to consume
his endowment?
(d)(3pt) Calculate the equilibrium interest rate.
3.A and B have a project each. A's project will earn $100x next year and B's
will earn ($2x-$100)*100, where x is a random variable with a mean E(x)>100.
To carry out the project, they need to raise funds from the market. They
decide to issue 100 stock shares each. Paying pa(pb), an investor receives
$x($2x-$100) next year. (Consider the share as a continuous variable.)
(a)(2pt) What is the rate of return of B's stock, rb? (It's a function of x
and pb)
(b)(2pt) Please calculate the correlation coefficient of the rate of return
of these two stocks, ρ(ra,rb).
(c)(2pt) In the following graph, σ and μ denote the standard deviation and
the mean of the rate of return. Point a(b) reflects the situation of A's
(B's) stock. For an investor who considers to purchase some share from A
and B, what is the collection of all the possible (σ,μ) of his
portfolio? Argue clearly, and draw your answer in a graph.
μ↑
│
│
│ ‧b
│ (編註:a,b,rf三者之間各以虛線連接且三點不共線)
│
│ ‧a
rf┤
│
└───────→
σ
(d)(2pt) The risk-free rate rf and is marked on the graph above. Could the
situation shown in the graph be an equilibrium? Why?
4.Suppose the reckless driving impose costs (in the form of medical bills) on
both the drivers themselves and on pedestrians. Each mile of reckless
driving costs drivers $1 and pedestrians $0.25. The marginal value of a
driver of his/her reckless driving is indicated by the downward-sloping
curve in the following figure. The drivers are not responsible for
pedestrians' losses. Answer the following questions in terms of labeled
areas on the graph.
↑
$/mile│╲
│Ａ╲
├──┬──┬──┬──┬─
│ │╲Ｄ│ │ │
│Ｂ │Ｃ╲│Ｅ │Ｆ │
├──┼──┼──┼──┼─
│ │ │╲Ｊ│ │ (編註:斜線即MV，為一連續線
│Ｇ │Ｈ │Ｉ╲│Ｋ │ 受限於bbs故以此表現)
├──┼──┼──┼──┼─
│ │ │ │╲Ｐ│
│Ｌ │Ｍ │Ｎ │Ｏ╲│
├──┼──┼──┼──┼─
│ │ │ │ │╲ MV
│Ｑ │Ｒ │Ｓ │Ｔ │
└──┴──┴──┴──┴─→
Miles of Reckless Driving
(a)(2pt) What is the social gain from a driver's reckless driving?
(b)Suppose drivers can acquire air bags that reduce the cost to them of
their reckless driving from $1 per mile to $0.5 per mile. The cost to
pedestrians remains $0.25 per mile, regardless of whether drivers use air
bags.
i.(2pt) What is the maximum price, pmax that a driver is willing to pay
for an air bag?
ii.(3pt) The market of air bags are competitive and an air bag is sold at
its cost cbag and cbag<pmax. How much would you like to tax an air bag
to make the transaction efficient, i.e. sales of air bags imply an
increase in the social gain?
5.In a city of 60 residents, there are 2 aquariums. Residents visit aquariums
every weekend without any other recreational alternatives. Each person will
decide which aquarium to visit this weekend and they all share the same
preference. The value of the visit depends on how many residents crowd in an
aquarium. When there are n person in aquarium A(B), the value of the visit
per person in monetary term is:
AVA=120-2nA,
AVB=60-nB.
(a)(2pt) In equilibrium, how many people will visit aquarium A?
(b)(4pt) If we want to maximize total value of visits, how many people
should be allowed to vist aquarium A? And to achieve this, how should you
charge an entry fee for a visit to aquarium A? (While the visit to
aquarium B remains free.)
(c)(2pt) If instead, the city wishes to maximize the total ticket revenue
from these two aquariums, what is the ticket price at each aquarium?
6.(2pt) Years after tears, rice is harvested in May and December. Suppose the
demend for each month is known. The monthly interest rate is a constant r.
The inventory cost is assumed zero. What is the relationship between the
rice price in February and the rice price in April?
(編註:暗字為下標)
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